1 Introduction

Ti–6Al–4V alloy which comes under the classification of α–β titanium (Ti) alloys has many applications aircraft manufacturing, chemical and biomedical industries due to its exceptional characteristics of high strength to density ratio, admirable resistance to corrosion resistance and high temperature withstanding capabilities [1,2,3]. Weldability of Ti–6Al–4V alloy is good compared to other Ti alloys so that this alloy is being welded for the fabrication of aeroengine components such as compressor blades, engine shrouds, airframes etc. Ti–6Al–4V alloy is an allotropic material in which Al and V acts as α and β stabilizers respectively. It can be strengthened by various heat treatment and strain hardening processes, in particular by solutionizing with subsequent quenching [4,5,6]. Moreover, this alloy is very sensitive to thermal cycles during welding, results in catastrophic variations in the microstructure [7, 8]. Electron beam welding (EBW) and laser beam welding (LBW) are considered as a perfect joining technique for Ti–6Al–4V alloys due to the specific advantages such as high depth of penetration, lesser welding defects and narrower HAZ and FZ compared to GTAW [9,10,11,12]. However, EBW process has some limitations such as requirement of vacuum environment and hazard of harmful emission of X-rays [13,14,15].

New techniques were developed in recent years to eliminate these limitations and most of them were derived from the basic GTAW technique which is highly economical compared to other techniques. One of the very significant derivatives of GTAW used in this investigation was Gas Tungsten Constricted Arc Welding (GTCAW) [16]. GTCAW works at a very high frequency (20 kHz) which is able to generate constricted arc by magnetic constriction with a columnar shape like plasma arc (Fig. 1). The arc constriction leads to narrow HAZ and FZ compared to conventional GTAW process [17, 18].

Fig. 1
figure 1

Schematic diagram of variants of GTAW used in this investigation

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Many optimization techniques were employed to determine the fusion zone (FZ) characteristics by the establishment of analytical models. Response surface methodology (RSM) was widely used for these kind of welding problems [19,20,21]. Few researchers [22, 23] studied about the impact of pulsed current influence on bead geometry on GTA welding parameters as well as Ti–6Al–4V alloy’s mechanical properties.

However, an available information in literature pertaining to GTCAW process parameters and fusion zone characteristics of titanium alloy joints is very scant. Most of the researchers have considered peak current, arc frequency, and welding speed as the input welding parameters but there is no systematic study reported involving “delta current or inter-pulse current and delta frequency or inter-pulse frequency” (important input welding parameters influencing the FZG and FZH). Hence this research work is emphasis on the optimization of essential GTCAW parameters to achieve minimum FZG and maximum FZH employing RSM.

2 Experimental

Ti–6Al–4V alloy sheets were cut into blanks (150 mm × 75 mm × 1.2 mm) for conducting welding experiments. Tables 1 and 2 shows base material chemical composition and mechanical properties.

Table 1 Chemical composition (wt%) of base alloy
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Table 2 Mechanical properties of base alloy
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2.1 Finding the working limits of the parameters

The quality of the joints was investigated throughout the trail runs with a combination of different process parameters. Figure 2 obviously highlights the issues come upon during the preliminary runs. By selecting suitable process parameters to overcome the issues to obtain defect free and quality joints.

Fig. 2
figure 2

Cause and effect diagram used for selection of process parameters for optimization

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The independently governable GTCAW parameters influence the grain size and hardness were resolved they are: peak current (IM), inter-pulse current (IP), inter-pulse frequency (IF), and welding speed (S). When detailing the working limits of the process parameters, + 2 are coded as upper limits and − 2 as lower limits. The in-between coded values were considered from the below relationship [24].

$$Z_{\text{i}} = 2\left[ {2{\text{Z}} - \left( {{\text{Z}}_{\hbox{max} } + {\text{ Z}}_{\hbox{min} } } \right)} \right]/\left( {{\text{Z}}_{\hbox{max} } - {\text{Z}}_{\hbox{min} } } \right)]$$
(1)

where Zi is the required coded value of variable Z; Z is any value of the variable from Zmin to Zmax; Zmin is the minimum value of the variable and Zmax is the maximum value of the variable (Table 3).

Table 3 Feasible GTCAW process parameters and their levels
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With help of central composite design (CCD) principle, an experimental design matrix was constructed (Table 4). As a result, 30 runs comprised of 16 factorial points, 8 star points and 6 center points. All the 30 runs are experimented and their actual responses were recorded. Analysing and interpolating the recorded responses yielded the relationship effects of the parameters on the FZG and FZH in linear, quadratic and two-way interaction models. All the experiments were carried out employing an Inter-pulse TIG welding machine capable of producing constricted arc.

Table 4 Design matrix and experimental results
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Metallographic specimens were collected from each joint using wire cut machining and the cross-section face of the specimens were polished using fine emery papers. The acetone-cleaned metallograhically polished specimens were etched using oxalic reagent to expose the FZ microstructure displayed in Fig. 3.

Fig. 3
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Micrograph of the fusion zone profiles

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2.2 Development of empirical relationship

FZG and FZH is a function of GTCAW parameters such as peak current (IM), inter-pulse current (IP), inter-pulse frequency (IF) and welding speed (S) and hence, it can be stated as

$${\text{Y}} = {\text{f}}\left( {{\mathbf{I}}_{{\mathbf{M}}} ,{\text{ I}}_{\text{P}} ,{\text{ I}}_{\text{F}} ,{\text{S}}} \right)$$
(2)
$${\rm {Y}} = {\rm {C}}_{0} + {\rm {C}}_{1} {\rm {I}}_{\rm {M}} + {\rm {C}}_{2} {\rm {I}}_{\rm {P}} + {\rm {C}}_{3} {\rm {I}}_{\rm {F}} + {\rm {C}}_{4} {\rm {S}} + {\rm {C}}_{11} {\rm {I}}_{\rm {M}}^{2} + {\rm {C}}_{22} {\rm {I}}_{\rm {P}}^{2} + {\rm {C}}_{33} {\rm {I}}_{\rm {F}}^{2} + {\rm {C}}_{44} {\rm {S}}^{2} + {\rm {C}}_{12} {\rm {I}}_{\rm {M}} {\rm {I}}_{\rm {P}} + {\rm {C}}_{13} {\rm {I}}_{\rm {M}} {\rm {I}}_{\rm {F}} + {\rm {C}}_{14} {\rm {I}}_{\rm {M}} {\rm {S}} + {\rm {C}}_{23} {\rm {I}}_{\rm {P}} {\rm {S}} + {\rm {C}}_{24} {\rm {I}}_{\rm {F}} {\rm {S}}$$
(3)

where C0 is the mean of response and C1, C2,…, C4, C11, C13,…, C34 are the coefficients that is based on the interaction and individual effects of parameters. Table 5 shows the calculated coefficients values from DESIGN EXPERT 9.0 software [25].

Table 5 Co-efficient and their estimated factors
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The empirical relationships to predict FZG and FZH were developed incorporating the values of coefficients. The developed empirical relationships are given below:

  • Fusion zone hardness (FZH) = {433.67 − 7.17 (IM) + 4.75 (IP) + 10.42 (IF) − 5.00 (S) − 1.88 (IMIP) − 2.38 (IMIF) + 3.00 (IMS) − 3.13 (IPIF) + 1.00 (IPS) + 1.75 (IFS) − 7.38 (I 2M ) − 10.75 (I 2P ) − 8.50 (I 2F ) − 7.50 (S2)} Hv

  • Fusion zone grain size (FZG) = {258.67 + 14.33 (IM) − 8.25 (IP) − 14.92 (IF) + 11.92 (S) − 0.87 (IMIP) + 2.75 (IMIF) − 6.25 (IMS) + 6.88 (IPIF) − 0.87 (IPS) − 8.25 (IFS) + 23.54 (I 2M ) + 25.29 (I 2P ) + 19.17 (I 2F ) + 20.67 (S2)} μm.

2.3 Checking adequacy of the developed relationships

The competence of the derived empirical relationships for determining the FZH and FZG of the GTCAW joints was confirmed by analysis of variance (ANOVA) method. According to this method, the calculated Fratio has to be less than the standard Fratio for the model to be satisfactory at 95% confidence level. The sum of squares, degrees of freedom and F value of the developed models and their interactions are represented in the Table 5.

The Model is found to be significant as the F value of the model is less than the 0.0001. This indicates that probability of occurrence of this much of larger F-value induced by noise is not more than 0.01%. The model terms which have p value less than 0.05 are considered as significant in the ANOVA tests. Thus the model terms namely IM, IP, S, IMS, IPIF, I 2M , I 2P , I 2F , S2 are found significant. In the ANOVA table, the lack of fit generally indicates the error in the model and it is very less (2.55) compared to the significant model terms. Thus lack of fit is insignificant. The“r2″ values which are termed as Coefficient of determination is calculated for both actual experiment and the developed model. The value of “r2” denotes the nearness between the predicted and experimental results. The adj.r2 of 0.9323 is relatively close to the pred.r2 of 0.8230. From the observations made on the ANOVA Tables 6 and 7, it is confirmed that the developed model and the empirical relationships are satisfactory. To validate the values predicted with the help of empirical relationship, three experiments were conducted and their results are presented in Table 8. The predicted and experimental values have small admissible difference of error.

Table 6 ANOVA test results for fusion zone hardness
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Table 7 ANOVA test results for fusion zone grain size
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Table 8 Validation of optimization procedures
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2.4 Relationship between fusion zone hardness and grain size

Figure 4 shows correlated graph of experimentally measured FZG and FZH values that is represented in Table 4. The entire points are allied by a best adequate straight line and the governing equation are given by

$${\text{FZH}}\,\left( {\text{Hv}} \right) = \left[ {547.77 - 0.42903 \, \left( {\text{FZG}} \right),\upmu{\text{m}}} \right]$$
(4)

The above equation represents the best adequate straight line as negative sign in the slope and this also suggested that the FZH was inversely proportional influence with fusion zone grain size. The above equation shows R2 is 96.2% as a coefficient of determination. The R2 in regression equation will provides an information about the goodness of the fit. The derived equation can be appropriated to determine the value of FZH for a given grain size.

Fig. 4
figure 4

Relationship between fusion zone hardness and fusion zone grain size

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3 Optimization of GTCA welding parameters

The empirical relationship was developed with help of RSM, via taking ‘X’ and ‘Y’ axis as a parameters and ‘Z’ axis as responses. The response surface represents the minimum toward maximum series of responses and shows the apex precisely which represents the optimum solution. In Fig. 5, the apex of response surface was executed by the optimum FZH and FZG of GTCA welded Ti–6Al–4V alloy. The spherical mound shape is illustrated on contour plot and the area of optimal feature settings is displayed with responses through independence factors. Response surface analysis initiate the contour plots with software, the outline of surface can be distinguished with help of rational accuracy which is positioned in optimum. The optimal parameters are shown in Figs. 5 and 6 with an arrow mark. Spherical shape contours are indicative of less interaction between parameters. However, elliptical shape contour are indicate of high interaction between parameters.

Fig. 5
figure 5

Response graph and contour plots for fusion zone grain size

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Fig. 6
figure 6

Response graph and contour plots for fusion zone hardness

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4 Analysis of response graphs and contour plots

Prior to optimization, it is necessary to illuminate the influence of GTCAW parameters on FZG and FZH. For this purpose, 3D contour plot and response graphs are constructed (see Figs. 5, 6).

Figures 5a and 6a illustrate the 3D response plots of FZG and FZH acquired from the model, considering as an inter-pulse frequency of 12 kHz and peak current of 50 A.

3D response plot clearly identify that when increasing inter-pulse frequency to 12 kHz, the FZG is finer. The coarser grains are formed at lower inter-pulse frequency, due to less rigorous stirring action of arc in weld pool [24]. Increasing the inter-pulse frequency beyond 12 kHz causes violent and more agitation of the arc in molten weld pool promotes finer grain as well as acicular alpha martensite (α′) structure, so FZH also higher in that region [11]. Hence, acicular alpha martensite (α′) are maximum in optimum inter-pulse frequencies. In this study, an optimum inter-pulse frequency is to be determined as 12 kHz.

Figures 5c and 6c demonstrate the 3D response graph of FZG and FZH acquired from the model, pretending a welding speed and peak current. From the 3D response graph, it is known that the FZG of joint welded at a 60 mm/min is finer and FZH of the joints is maximum. The acicular alpha (α′) martensites were bundled in the FZ and this may be accountable for higher hardness of these joints. The lower welding speed yields high heat input in the FZ, which considerably produce coarser grains as well as basket weave structure and reduces the hardness [6]. While increasing the welding speed, the heat input lowers and this causes increase in hardness and the formation of fine grains [14]. Subsequently with high welding speed (above 55–60 mm/min) better quality GTCAW joints are obtained. Few additional joints were produced just beyond the parameters for confirming the rationality of the optimization techniques. Table 8 represent the validation results. An optimization procedures are realistic in this study are concluded from the results.

Figure 7 shows BM optical micrograph (OM) and scanning electron micrographs (SEM) and FZ of the joints fabricated with the optimized parameter (IM = 50 A, IP = 30 A, IF = 12 kHz and S = 60 mm/min). The formation of finer grains as well as acicular alpha (α′) martensite in fusion zone is main reasons for higher hardness and minimum fusion zone grain size in these joints [7, 8].

Fig. 7
figure 7

Microstructural features of optimized joint: a optical microstructure of base metal. b SEM of base metal. c Transition zone (OM). d Fusion zone (SEM). e Fusion zone (OM). f Heat affected zone (OM)

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5 Conclusions

  1. 1.

    Empirical relations were established to assess the fusion zone grains (FZG) and fusion zone hardness (FZH) of Ti–6Al–4V alloy joints.

  2. 2.

    From ANOVA test results, it is found that the inter-pulse frequency is highly significant GTCAW parameter (F = 222.87) and delta current is less significant parameter (F = 68.17).

  3. 3.

    Minimum FZG of 253 µm and maximum FZH of 439 Hv were attained under the welding conditions (IM = 50 A, IP = 30 A, IF = 12 kHz and S = 60 mm/min). These set of welding parameters are identified as an optimum GTCAW parameters to attain minimum FZG and maximum FZH with full penetration in 1.2 mm thin sheets of Ti–6Al–4V alloy employed in aero-engine applications.

  4. 4.

    An empirical relationship was developed relating FZG and FZH and this relationship can be effectively used to predict FZG from FZH.